What makes this a vicious cycle is that, in the short term, each of the above has reasonable motivations and is making a reasonable decision. The vandal is just having 'fun' of some sort, and to his or her point of view, that's what Wikipedia is for: fun. The sysop is trying to put out fires, may consider himself or herself part of a en:Wikipedia:Volunteer fire department, and doesn't care to distinguish vandals from trolls or (quite often) just those contributors whose political opinions the sysop doesn't like. This drives away contributors who are mistaken for vandals, who are caught out in some 'rule' they don't understand, or who are just disgusted with lack of accountability of sysops. So this is already a vicious cycle - let's call it the Sysop-Vandal cycle.

Then, add in the troll who tries to somehow alter this power balance by going after specific sysops who she or he perceives as more oppressive or stupid or biased (call this the Sysop-Troll cycle), and you have recipes for more conflicts (the whole Vandal-Sysop-Troll Wikipedia vicious cycle) that can't clearly be said to drive out more contributors, or fewer, than Vandal-Sysop alone. The trolls probably think they themselves do good. The sysops probably think the trolls do harm. Who cares what they think? It's what they do, that does the damage.

Perhaps a Wikipedia Peace Process is required to dampen the enthusiasm of sysops and trolls for attacking each other, so sysops can concentrate on dealing with actual vandals, and trolls can attack some less petty power clique which might (hint!) be a better use of their time.